To find the slope of a line passing through two points, $(x_1, y_1)$ and $(x_2, y_2)$, we use the formula:

$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$

Given the points $(2, 5)$ and $(8, -4)$:

1. Let $(x_1, y_1) = (2, 5)$ and $(x_2, y_2) = (8, -4)$.
2. Substitute these values into the formula:

$\text{slope} = \frac{-4 - 5}{8 - 2} = \frac{-9}{6} = -\frac{3}{2}$

So, the slope of the line passing through the points $(2, 5)$ and $(8, -4)$ is $-\frac{3}{2}$.

Would you like further details on this calculation or have any other questions?

Here are some related questions you might find useful:

1. How do you find the slope if one of the points has a zero coordinate?
2. What happens to the slope if both points lie on the same horizontal line?
3. How does the slope formula change if we reverse the points?
4. What does a slope of $-\frac{3}{2}$ indicate about the line's direction?
5. How would you find the equation of the line given these points?

Tip: A negative slope indicates that the line is sloping downwards from left to right.